To find : the real solution of the polynomial function
Answer to Problem 29E
The real solution of the polynomial function is:
Explanation of Solution
Given information:
Concept Involved:
The Rational Zero Test : The Rational Zero Test relates the possible rational zeros of a polynomial (havinginteger coefficients) to the leading coefficient and to the constant term of the polynomial.
If the polynomial
To use the Rational Zero Test, you should first list all rational numbers whosenumerators are factors of the constant term and whose denominators are factors of theleading coefficient.
Possible rational zeros:
Synthetic Division (for a Cubic Polynomial):To divide
In case when we have a polynomial with a missing term, insert placeholders with zero coefficients for missing powers of the variable. Vertical pattern: Add terms in columns Diagonal pattern: Multiply results by k. This algorithm for synthetic division works only for divisors of the form x - k. Remember that |
The Division Algorithm: If
Graph:
Interpretation:
From the graph of the function we can pick possible zeros of the function as
Calculation:
Identify the polynomial by bringing all the terms to left side of the equation and write it in the form
Identifying the constant and leading coefficient of the given function
Constant is
Leading coefficient is
Listing the factors of constant
Listing the factors of Leading Coefficient -5:
The possible rational zeros of the function are:
If
To find other zeros of the polynomial
Use the quadratic formula
Simplify the expression inside the square root
Simplify the radical by splitting 76 as product of two numbers out of one is square number.
Cancel the common factor in the numerator and denominator to get the final answer
Conclusion:
The possible rational zeros of the function are:
The actual rational zeros of the function are:
The real solution of the polynomial function is:
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning